Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C2×C19×#1315 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C23×C19 | C22⋊C8 |
| prime radical | C22×#41×C19 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C23×C8×C19 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61);(3,4)(5,9,10,7)(6,8)(11,12,15,20,16,21,30,38,17,22,31,39,14,19,28,36)(13,23,25,40,24,34,41,37,26,35,29,42,27,18,32,33);(3,5)(4,7)(6,10)(8,9)(11,13)(12,18)(14,27)(15,29)(16,24)(17,26)(19,35)(20,37)(21,23)(22,34)(25,31)(28,41)(30,32)(33,39)(36,40)(38,42)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4408);